Here we report on a precise study of the ratio of elastic scattering cross sections of electrons and positrons from $\sp{12}$C and $\sp{208}$Pb, in an effort to observe and quantify deviations from the predictions of a phase shift calculation of the scattering from a static charge density. Any deviations observed can be attributed to higher-order processes sensitive to the sign of the charge of the scattered particle. The beam energies were $\sim$450 MeV and the angular ranges covered were 26-37$\sp\circ$ for $\sp{12}$C and 26-53$\sp\circ$ for $\sp{208}$Pb. No deviations were observed within the uncertainties of the measurement.